Li and co-workers recently developed a dual C-H bond activation strategy, using a Rh(III) catalyst, for [3 + 2]/[5 + 2] annulation of primary 4-aryl-1,2,3-triazoles and alkynes. The Rh(III)-catalyzed dual annulation of 4-aryl-1,2,3-triazoles and alkynes is challenging because only single annulation is achieved using Rh(II) and Ni(0) catalysts. Intrigued by the novel strategy, we performed a density functional theory study to unravel this challenging dual C-H bond activation. A Friedel-Crafts type mechanism proved be more favorable than a concerted metalation-deprotonation (CMD) mechanism for the first C-H bond activation. The second C-H bond activation proceeded via a CMD mechanism. More importantly, the calculation explained why only AgSbF6, among several candidates, performed perfectly, whereas others failed, and why the dual annulation of 4-aryl-1,2,3-triazoles with alkynes was achieved with a Rh(III) catalyst but not with Rh(II) and Ni(0) catalysts. Due to the active catalyst being [Cp*Rh(OAc)]+, AgSbF6, in which SbF6- is a stable anion, among several candidates performed perfectly. The success of the Rh(III)-catalyzed dual C-H bond activation has two origins: (i) the active catalyst [Cp*Rh(OAc)]+ is more stable than Cp*Rh(OAc)2 when the Ag salt is AgSbF6, and this facilitates the first alkyne insertion; and (ii) a rhodium-carbene is easily formed.